
Signed graphs are another interesting variation of graphs, usually taken to be graphs in which each edge is either positive or negative. In the literature, there is more than one option for the rule for the labels on the edges of the line graph, and two of these will be considered here. It is therefore useful for us to use different symbols for the signs in the two cases, and hence different arithmetic formulas for the line-graph rule. In the first kind, we use + and − with the rule being the common product of signs. The focus in the resulting signed line graph is whether all cycles have a positive value. In the second, we use 0 and 1 and the rule is the Boolean binary sum. The focus in the resulting signed line graph is on Boolean properties and special colorings.
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